Claude Meunier

Synchrony in excitatory neural networks

Synchronization properties of fully connected networks of identical oscillatory neurons are studied, assuming purely excitatory interactions. We analyze their dependence on the time course of the synaptic interaction and on the response of the neurons to small depolarizations. Two types of responses are distinguished. In the first type, neurons always respond to small depolarization by advancing the next spike. In the second type, an excitatory postsynaptic potential (EPSP) received after the refractory period delays the firing of the next spike, while an EPSP received at a later time advances the firing. For these two types of responses we derive general conditions under which excitation destabilizes in-phase synchrony. We show that excitation is generally desynchronizing for neurons with a response of type I but can be synchronizing for responses of type II when the synaptic interactions are fast. These results are illustrated on three models of neurons: the Lapicque integrate-and-fire model, the model of Connor et al., and the Hodgkin-Huxley model. The latter exhibits a type II response, at variance with the first two models, that have type I responses. We then examine the consequences of these results for large networks, focusing on the states of partial coherence that emerge. Finally, we study the Lapicque model and the model of Connor et al. at large coupling and show that excitation can be desynchronizing even beyond the weak coupling regime.

On numerical simulations of integrate-and-fire neural networks

It is shown that very small time steps are required to reproduce correctly the synchronization properties of large networks of integrate-and-fire neurons when the differential system describing their dynamics is integrated with the standard Euler or second-order Runge-Kutta algorithms. The reason for that behavior is analyzed, and a simple improvement of these algorithms is proposed.

Phase Dynamics for Weakly Coupled Hodgkin-Huxley Neurons

Hodgkin-Huxley model neurons coupled by weak excitatory interactions are studied by a phase reduction technique. All the information about the coupling between the neurons and their synchronization is then contained in an effective interaction between their phases. One shows analytically that an excitatory coupling can result in an effective inhibition between the neurons reducing their firing rates. Systems of two neurons exhibit bistability and out-of-phase locking. It is suggested that these features may have significant consequences for networks.

Synchrony in Heterogeneous Networks of Spiking Neurons

The emergence of synchrony in the activity of large, heterogeneous networks of spiking neurons is investigated. We define the robustness of synchrony by the critical disorder at which the asynchronous state becomes linearly unstable. We show that at low firing rates, synchrony is more robust in excitatory networks than in inhibitory networks, but excitatory networks cannot display any synchrony when the average firing rate becomes too high. We introduce a new regime where all inputs, external and internal, are strong and have opposite effects that cancel each other when averaged. In this regime, the robustness of synchrony is strongly enhanced, and robust synchrony can be achieved at a high firing rate in inhibitory networks. On the other hand, in excitatory networks, synchrony remains limited in frequency due to the intrinsic instability of strong recurrent excitation.

Resonant or Not, Two Amplification Modes of Proprioceptive Inputs by Persistent Inward Currents in Spinal Motoneurons

Why do motoneurons possess two persistent inward currents (PICs), a fast sodium current and a slow calcium current? To answer this question, we replaced the natural PICs with dynamic clamp-imposed artificial PICs at the soma of spinal motoneurons of anesthetized cats. We investigated how PICs with different kinetics (1–100 ms) amplify proprioceptive inputs. We showed that their action depends on the presence or absence of a resonance created by the Ih current. In resonant motoneurons, a fast PIC enhances the resonance and amplifies the dynamic component of Ia inputs elicited by ramp-and-hold muscle stretches. This facilitates the recruitment of these motoneurons, which likely innervate fast contracting motor units developing large forces, e.g., to restore balance or produce ballistic movements. In nonresonant motoneurons, in contrast, a fast PIC easily triggers plateau potentials, which leads to a dramatic amplification of the static component of Ia inputs. This likely facilitates the recruitment of these motoneurons, innervating mostly slowly contracting and fatigue-resistant motor units, during postural activities. Finally, a slow PIC may switch a resonant motoneuron to nonresonant by counterbalancing Ih, thus changing the action of the fast PIC. A modeling study shows that Ih needs to be located on the dendrites to create the resonance, and it predicts that dendritic PICs amplify synaptic input in the same manner as somatic PICs.

Mixed Mode Oscillations in Mouse Spinal Motoneurons Arise from a Low Excitability State

We explain the mechanism that elicits the mixed mode oscillations (MMOs) and the subprimary firing range that we recently discovered in mouse spinal motoneurons. In this firing regime, high-frequency subthreshold oscillations appear a few millivolts below the spike voltage threshold and precede the firing of a full blown spike. By combining intracellular recordings in vivo (including dynamic clamp experiments) in mouse spinal motoneurons and modeling, we show that the subthreshold oscillations are due to the spike currents and that MMOs appear each time the membrane is in a low excitability state. Slow kinetic processes largely contribute to this low excitability. The clockwise hysteresis in the I–F relationship, frequently observed in mouse motoneurons, is mainly due to a substantial slow inactivation of the sodium current. As a consequence, less sodium current is available for spiking. This explains why a large subprimary range with numerous oscillations is present in motoneurons displaying a clockwise hysteresis. In motoneurons whose I–F curve exhibits a counterclockwise hysteresis, it is likely that the slow inactivation operates on a shorter time scale and is substantially reduced by the de-inactivating effect of the afterhyperpolarization (AHP) current, thus resulting in a more excitable state. This accounts for the short subprimary firing range with only a few MMOs seen in these motoneurons. Our study reveals a new role for the AHP current that sets the membrane excitability level by counteracting the slow inactivation of the sodium current and allows or precludes the appearance of MMOs.

Sparsely coded associative memories: capacity and dynamical properties

We consider very sparsely coded associative memories of binary neurons, for both Hebbian and covariant learning rules. We calculate explicitly their maximal capacity both in terms of patterns, and in terms of information content, taking into account the correlation of local fields, and we investigate its dependence on the degree of sparsity. The sparseness of the coding enhances both the memory capacity and the information capacity, whatever the chosen scheme. The study of the retrieval dynamics shows that, as soon as the number of patterns stored exceeds some critical value, retrieval becomes limited to the states with the same activity as the prototype patterns.

How Much Afterhyperpolarization Conductance Is Recruited by an Action Potential? A Dynamic-Clamp Study in Cat Lumbar Motoneurons

We accurately measured the conductance responsible for the afterhyperpolarization (medium AHP) that follows a single spike in spinal motoneurons of anesthetized cats. This was done by using the dynamic-clamp method. We injected an artificial current in the neurons that increased the AHP amplitude, and we made use of the fact that the intensity of the natural AHP current at the trough of the voltage trajectory was related linearly to the AHP amplitude. We determined at the same time the conductance and the reversal potential of the AHP current. This new method was validated by a simple theoretical model incorporating AHP and hyperpolarization-activated (Ih) currents and could be applied when the decay time constant of the AHP conductance was at least five times shorter than the estimated Ih activation time. This condition was fulfilled in 33 of 44 motoneurons. The AHP conductance varied from 0.3 to 1.4 μS in both slow- and fast-type motoneurons, which was approximately the same range as the input conductance of the entire population. However, AHP and input conductances were not correlated. The larger AHP in slow-type motoneurons was mainly attributable to their smaller input conductance compared with fast motoneurons. The likeness of the AHP conductance in both types of motoneurons is in sharp contrast to differences in AHP decay time and explains why slow- and fast-type motoneurons have similar gain.

Reduction of Presynaptic Action Potentials by PAD: Model and Experimental Study

A compartmental model of myelinated nerve fiber was used to show that primary afferent depolarization (PAD), as elicited by axo-axonic synapses, reduces the amplitude of propagating action potentials primarily by interfering with ionic current responsible for the spike regeneration. This reduction adds to the effect of the synaptic shunt, increases with the PAD amplitude, and occurs at significant distances from the synaptic zone. PAD transiently enhances the sodium current activation, which partly accounts for the PAD-induced fiber hyperexcitability, and enhances sodium inactivation on a slower time course, thus reducing the amplitude of action potentials. In vivo, intra-axonal recordings from the intraspinal portion of group I afferent fibers were carried out to verify that depolarizations reduced the amplitude of propagating action potentials as predicted by the model. This article suggests PAD might play a major role in presynaptic inhibition.

Two and three dimensional reductions of the Hodgkin-Huxley system: separation of time scales and bifurcation schemes

We study two different two-dimensional reductions of the Hodgkin-Huxley equations. We show that they display the same qualitative bifurcation scheme as the original equations but overestimate the current range where periodic emission occurs. This is essentially due to the assumption that the evolution of the sodium activation variable m is instantaneous with respect to the dynamics of the variables h and n, an hypothesis that breaks down at high values of the injected current. To prove this point we compare the current-amplitude relation, the current-frequency relation, and the shapes of individual spikes for the two reduced models to the results obtained for the original Hodgkin-Huxley model and for a three dimensional model with instantaneous sodium activation. We show that a more satisfying agreement with the original Hodgkin-Huxley equations is obtained if we modify the evolution equation for the potential by incorporating the prominent features of the dynamics of m.